Team specific work item types

You can control who can create work items of a specific set of types in a role-based way ... i.e. you can have a task-creator role, and assign that to the people that are allowed to create tasks, and a defect-creator role, and assign that to the people that are allowed to create defects.
You also can control who can see existing work items, by indicating that work items assigned to a particular team should only be visible to members of that team.
But I am not aware of any out-of-the-box way of hiding the existence of a particular work item type from just some teams in a project area but not others.

workitems are project wide.

you can limit visibility by team but its ALL workitems for a team..
team A can't see Team B's work, and vice versa.. but its ALL workitems

It seems there is no direct way to restrict a whole work item type but you can try either by Restricted Access presentation or by creating WorkItem Categories to restrict access to work items.

Although not tested, but you may try to combine workitem categories and use calculated value script to automatically fill the FiledAgainst attribute depending on the workitem.Type

Thanks Geoffrey, Sam and Indradri for your answers! This pretty much confirms the behavior that I'm seeing. I just wanted to have as much isolation as possible between teams in one project to avoid confusion.